In the present paper we focused on the MEE in a \(XY\)  chain, which was introduced in seminal paper of Lieb, Schulz and Mattis [1]}. As KNB mechanism is essentially affected by the physical form of the lattice, the simplest case corresponds to the linear arrangement of spins, which features the polarization given in equation (REF ). Then, seeking for exactly solvable case we have to chose an electric field to be pointed in \(y\) -direction. This leads to a model of \(XY\)  chain with DM terms, when DM-vector is parallel to \(z\) -axis. This model is well known [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]}, [19]}, however, for the last half-century quite restricted amount of papers have been devoted to it. The paper is organized as follows: in the second Section the formulation of the model and its exact solution in terms of Jordan-Wigner fermionization is given, in the next Section the zero temperature MEE for the simplest model of MEE in quantum spin chains are described, then the finite temperature MEE and effects of the \(XY\)  anisotropy \(\gamma \)  are analyzed. The paper is ended with a Conclusion.
